Distorted well pressure correction

Abstract

Method and system for developing reservoirs, such as hydrocarbon reservoirs or aquifers, including correcting pressure transient test data to account for variations of fluid density between a gauge depth and a mid-reservoir depth in a wellbore. Gauge depth pressure and temperature measurements, and density correlations are used to estimate mid-reservoir depth pressures, which can be used in a pressure transient analysis.

What is claimed is: 
     
       1. A method of developing a reservoir, the method comprising:
 obtaining transient pressure test data comprising gauge depth measurements at a gauge depth for a wellbore of a well extending into the reservoir, the gauge depth located at a distance above a mid-reservoir depth in the wellbore, the gauge depth measurements comprising, for each of different instants of time of a time period:
 a measurement of pressure obtained by way of a pressure gauge located at the gauge depth in the wellbore; and 
 a measurement of temperature obtained by way of a temperature gauge located at the gauge depth in the wellbore, 
 
 determining a depth interval extending between the gauge depth and the mid-reservoir depth in the wellbore; 
 dividing the depth interval into a series of consecutive nodes extending across the depth interval, wherein each node of the series of consecutive nodes represents a respective depth within the depth interval, wherein a first node of the series of consecutive nodes corresponds to the gauge depth and a last node of the series of consecutive nodes corresponds to the mid-reservoir depth, and intermediate nodes are defined by nodes located between the first node and the last node; 
 for each instant of time of the instants of time:
 determining, based on the measurement of pressure for the instant of time and the measurement of temperature for the instant of time, a first density of wellbore fluid; 
 associating, with the first node of the series of consecutive nodes, the measurement of pressure for the instant of time, the measurement of temperature for the instant of time, and the first density of wellbore fluid; 
 for each intermediate node:
 determining, based on the measurement of temperature for the instant of time associated with the first node, an estimated temperature for the intermediate node and associating the estimated temperature with the intermediate node; and 
 determining, based on the estimated temperature for the intermediate node, an estimated density for the intermediate node and associating the estimated density with the intermediate node; 
 
 determining, based on the measurement of temperature for the instant of time associated with the first node, an estimated temperature at the mid-reservoir depth and associating the estimated temperature with the last node; 
 determining, based on the estimated temperature at the mid-reservoir depth associated with the last node, an estimated density for the last node and associating the estimated density with the last node; 
 for each node of the intermediate nodes and the last node:
 determining, based on the estimated density associated with the node, an estimated pressure for the node and associating the estimated pressure with the node; 
 
 for each of pair of consecutive nodes of the series of consecutive nodes, determining an absolute difference between the estimated pressures associated with the pair of consecutive nodes; 
 determining a sum of the absolute differences; 
 determining whether the sum of the absolute differences is below a specified tolerance value; 
 in response to determining that the sum of the absolute differences is below the specified tolerance value, determining the estimated pressure associated with the last node to be a corrected mid-reservoir pressure for the instant of time; 
 
 determining, based on the corrected mid-reservoir pressures determined for the instants of time, corrected pressure transient test data comprising a corrected mid-reservoir pressure profile for the time period comprising the corrected mid-reservoir pressures determined for the instants of time; 
 determining, based on the corrected pressure transient test data, a reservoir development parameter; and 
 developing the reservoir based on the reservoir development parameter. 
 
     
     
       2. The method of  claim 1 , wherein the specified tolerance value is user specified. 
     
     
       3. The method of  claim 1 , wherein the specified tolerance value is in a range of 10 −8  to 10 −5  pounds per square inch. 
     
     
       4. The method of  claim 1 ,
 wherein determining the reservoir development parameter comprises conducting a pressure transient analysis of the mid-reservoir pressure profile for the time period to determine a derivative of pressure over the time period, and 
 wherein the reservoir development parameter is determined based on the derivative of pressure over the time period. 
 
     
     
       5. The method of  claim 1 , wherein the reservoir development parameter comprises a well operating pressure or a well operating flow rate, and wherein developing the reservoir comprises operating the well in accordance with the well operating pressure or the well operating flow rate. 
     
     
       6. The method of  claim 1 , wherein the reservoir comprises a hydrocarbon reservoir or an aquifer. 
     
     
       7. A reservoir development system, comprising:
 a pressure gauge located at a gauge depth in a wellbore of a well extending into a reservoir, the gauge depth located at a distance above a mid-reservoir depth in the wellbore; 
 a temperature gauge located at the gauge depth in the wellbore; and 
 a well control system configured to perform the following operations: 
 obtaining transient pressure test data comprising gauge depth measurements for the wellbore, the gauge depth measurements comprising, for each of different instants of time of a time period:
 a measurement of pressure obtained by way of the pressure gauge located at the gauge depth in the wellbore; and 
 a measurement of temperature obtained by way of the temperature gauge located at the gauge depth in the wellbore, 
 
 determining a depth interval extending between the gauge depth and the mid-reservoir depth in the wellbore; 
 dividing the depth interval into a series of consecutive nodes extending across the depth interval, wherein each node of the series of consecutive nodes represents a respective depth within the depth interval, wherein a first node of the series of consecutive nodes corresponds to the gauge depth and a last node of the series of consecutive nodes corresponds to the mid-reservoir depth, and intermediate nodes are defined by nodes located between the first node and the last node; 
 for each instant of time of the instants of time:
 determining, based on the measurement of pressure for the instant of time and the measurement of temperature for the instant of time, a first density of wellbore fluid; 
 associating, with the first node of the series of consecutive nodes, the measurement of pressure for the instant of time, the measurement of temperature for the instant of time, and the first density of wellbore fluid; 
 for each intermediate node:
 determining, based on the measurement of temperature for the instant of time associated with the first node, an estimated temperature for the intermediate node and associating the estimated temperature with the intermediate node; and 
 determining, based on the estimated temperature for the intermediate node, an estimated density for the intermediate node and associating the estimated density with the intermediate node; 
 
 determining, based on the measurement of temperature for the instant of time associated with the first node, an estimated temperature at the mid-reservoir depth and associating the estimated temperature with the last node; 
 determining, based on the estimated temperature at the mid-reservoir depth associated with the last node, an estimated density for the last node and associating the estimated density with the last node; 
 for each node of the intermediate nodes and the last node:
 determining, based on the estimated density associated with the node, an estimated pressure for the node and associating the estimated pressure with the node; 
 
 for each pair of consecutive nodes of the series of consecutive nodes, determining an absolute difference between the estimated pressures associated with the pair of consecutive nodes; 
 determining a sum of the absolute differences; 
 determining whether the sum of the absolute differences is below a specified tolerance value; 
 in response to determining that the sum of the absolute differences is below the specified tolerance value, determining the estimated pressure associated with the last node to be a corrected mid-reservoir pressure for the instant of time; 
 
 determining, based on the corrected mid-reservoir pressures determined for the instants of time, corrected pressure transient test data comprising a corrected mid-reservoir pressure profile for the time period comprising the corrected mid-reservoir pressures determined for the instants of time; 
 determining, based on the corrected pressure transient test data, a reservoir development parameter; and 
 developing the reservoir based on the reservoir development parameter. 
 
     
     
       8. The system of  claim 7 , wherein the specified tolerance value is user specified. 
     
     
       9. The system of  claim 7 , wherein the specified tolerance value is in a range of 10 −8  to 10 −5  pounds per square inch. 
     
     
       10. The system of  claim 7 ,
 wherein determining the reservoir development parameter comprises conducting a pressure transient analysis of the mid-reservoir pressure profile for the time period to determine a derivative of pressure over the time period, and 
 wherein the reservoir development parameter is determined based on the derivative of pressure over the time period. 
 
     
     
       11. The system of  claim 7 , wherein the reservoir development parameter comprises a well operating pressure or a well operating flow rate, and wherein developing the reservoir comprises controlling operation of the well in accordance with the well operating pressure or the well operating flow rate. 
     
     
       12. The system of  claim 7 , wherein the reservoir comprises a hydrocarbon reservoir or an aquifer. 
     
     
       13. A non-transitory computer readable storage medium comprising program instructions stored thereon that are executable by a processor to cause operations for developing a reservoir, the operations comprising:
 obtaining transient pressure test data comprising gauge depth measurements at a gauge depth for a wellbore of a well extending into the reservoir, the gauge depth located at a distance above a mid-reservoir depth in the wellbore, the gauge depth measurements comprising, for each of different instants of time of a time period:
 a measurement of pressure obtained by way of a pressure gauge located at the gauge depth in the wellbore; and 
 a measurement of temperature obtained by way of a temperature gauge located at the gauge depth in the wellbore, 
 
 determining a depth interval extending between the gauge depth and the mid-reservoir depth in the wellbore; 
 dividing the depth interval into a series of consecutive nodes extending across the depth interval, wherein each node of the series of consecutive nodes represents a respective depth within the depth interval, wherein a first node of the series of consecutive nodes corresponds to the gauge depth and a last node of the series of consecutive nodes corresponds to the mid-reservoir depth, and intermediate nodes are defined by nodes located between the first node and the last node; 
 for each instant of time of the instants of time:
 determining, based on the measurement of pressure for the instant of time and the measurement of temperature for the instant of time, a first density of wellbore fluid; 
 associating, with the first node of the series of consecutive nodes, the measurement of pressure for the instant of time, the measurement of temperature for the instant of time, and the first density of wellbore fluid; 
 for each intermediate node:
 determining, based on the measurement of temperature for the instant of time associated with the first node, an estimated temperature for the intermediate node and associating the estimated temperature with the intermediate node; and 
 determining, based on the estimated temperature for the intermediate node, an estimated density for the intermediate node and associating the estimated density with the intermediate node; 
 
 determining, based on the measurement of temperature for the instant of time associated with the first node, an estimated temperature at the mid-reservoir depth and associating the estimated temperature with the last node; 
 determining, based on the estimated temperature at the mid-reservoir depth associated with the last node, an estimated density for the last node and associating the estimated density with the last node; 
 for each node of the intermediate nodes and the last node:
 determining, based on the estimated density associated with the node, an estimated pressure for the node and associating the estimated pressure with the node; 
 
 for each of pair of consecutive nodes of the series of consecutive nodes, determining an absolute difference between the estimated pressures associated with the pair of consecutive nodes; 
 determining a sum of the absolute differences; 
 determining whether the sum of the absolute differences is below a specified tolerance value; 
 in response to determining that the sum of the absolute differences is below the specified tolerance value, determining the estimated pressure associated with the last node to be a corrected mid-reservoir pressure for the instant of time; 
 
 determining, based on the corrected mid-reservoir pressures determined for the instants of time, corrected pressure transient test data comprising a corrected mid-reservoir pressure profile for the time period comprising the corrected mid-reservoir pressures determined for the instants of time; 
 determining, based on the corrected pressure transient test data, a reservoir development parameter; and 
 developing the reservoir based on the reservoir development parameter. 
 
     
     
       14. The non-transitory computer readable storage medium of  claim 13 , wherein the specified tolerance value is user specified. 
     
     
       15. The non-transitory computer readable storage medium of  claim 13 , wherein the specified tolerance value is in a range of 10 −8  to 10 −5  pounds per square inch. 
     
     
       16. The non-transitory computer readable storage medium of  claim 13 ,
 wherein determining the reservoir development parameter comprises conducting a pressure transient analysis of the mid-reservoir pressure profile for the time period to determine a derivative of pressure over the time period, and 
 wherein the reservoir development parameter is determined based on the derivative of pressure over the time period. 
 
     
     
       17. The non-transitory computer readable storage medium of  claim 13 , wherein the reservoir development parameter comprises a well operating pressure or a well operating flow rate, and wherein developing the reservoir comprises controlling operation of the well in accordance with the well operating pressure or the well operating flow rate. 
     
     
       18. The non-transitory computer readable storage medium of  claim 13 , wherein the reservoir comprises a hydrocarbon reservoir or an aquifer. 
     
     
       19. A method of developing a reservoir, the method comprising:
 obtaining transient pressure test data comprising gauge depth measurements at a gauge depth for a wellbore of a well extending into the reservoir, the gauge depth located at a distance above a mid-reservoir depth in the wellbore, the wellbore gauge depth measurements comprising, for each of different instants of time of a time period:
 a measurement of pressure obtained by way of a pressure gauge located at the gauge depth in the wellbore; and 
 a measurement of temperature obtained by way of a temperature gauge located at the gauge depth in the wellbore, 
 
 dividing a depth interval extending between the gauge depth and the mid-reservoir depth in the wellbore into a series of consecutive nodes extending across the depth interval, wherein each node of the series of consecutive nodes represents a respective depth within the depth interval, wherein a first node of the series of consecutive nodes corresponds to the gauge depth and a last node of the series of consecutive nodes corresponds to the mid-reservoir depth, and intermediate nodes are defined by nodes located between the first node and the last node; 
 for each instant of time of the instants of time:
 determining, based on the measurement of pressure for the instant of time and the measurement of temperature for the instant of time, a first density of wellbore fluid; 
 for each intermediate node:
 determining, based on the measurement of temperature for the instant of time, an estimated temperature for the intermediate node; and 
 determining, based on the estimated temperature for the intermediate node, an estimated density for the intermediate node; 
 
 determining, based on the measurement of temperature for the instant of time, an estimated density for the last node; 
 for each node of the intermediate nodes and the last node:
 determining, based on the estimated density associated with the node, an estimated pressure for the node; 
 
 
 determining, based on the estimated pressures determined for the instants of time, corrected pressure transient test data comprising a corrected mid-reservoir pressure profile for the time period comprising the estimated pressures determined for the instants of time; 
 determining, based on the corrected pressure transient test data, a reservoir development parameter; and 
 developing the reservoir based on the reservoir development parameter.